A090089 Smallest even pseudoprimes to odd base=4n-1, not necessarily exceeding n.

286, 6, 10, 14, 6, 22, 26, 6, 34, 38, 6, 46, 10, 6, 58, 62, 6, 10, 74, 6, 82, 86, 6, 94, 14, 6, 106, 10, 6, 118, 122, 6, 10, 134, 6, 142, 146, 6, 14, 158, 6, 166, 10, 6, 178, 14, 6, 10, 194, 6, 202, 206, 6, 214, 218, 6, 226, 10, 6, 14, 22, 6, 10, 254, 6, 262, 14, 6, 274, 278, 6

Offset

1,1

Comments

There are no even pseudoprimes to an even base.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n)=Min{x=4n-1 number; Mod[ -1+n^(x-1), x]=0}

Example

n=1: base = 4n-1=3, smallest relevant power is -1+2^(286-1) which is divisible by 286.
Sieving further residue classes, smallest regularly arising pseudoprimes are 6,10 etc..

Mathematica

a[n_] := Module[{k = 2}, While[GCD[n, k] > 1 || PrimeQ[k] || PowerMod[n, k - 1, k] != 1, k += 2]; k]; Table[a[4*n - 1], {n, 1, 100}] (* Amiram Eldar, Nov 11 2019 *)

Crossrefs

Cf. A007535, A090085, A090986, A090087, A090088.

Sequence in context: A231422 A146893 A353544 * A204379 A025384 A256000

Adjacent sequences: A090086 A090087 A090088 * A090090 A090091 A090092

Keyword

nonn

Author

Labos Elemer, Nov 25 2003

Status

approved